Year 7: Numeric Substitution in Algebraic Expressions

Quick Reference

Substitute: Replace variables with their values
Follow BODMAS: Brackets, Orders, Division, Multiplication, Addition, Subtraction
Use brackets: When substituting negative numbers

What is Numeric Substitution?

Numeric substitution means replacing variables (letters) with given numbers in an expression, then calculating the result. It works with any complexity of expression.

Steps for Numeric Substitution

Identify all variables: Find all the letters in the expression
Replace each variable: Substitute each variable with its given value (use brackets for negative numbers)
Simplify: Follow order of operations (BODMAS/PEMDAS)

Examples with Different Complexities

Example 1: Simple - Find $2 x + 3$ when $x = 4$

$2 (4) + 3 = 8 + 3 = 11$

Example 2: With powers - Find $x^{2} + 5$ when $x = 3$

${(3)}^{2} + 5 = 9 + 5 = 14$

Example 3: Multiple variables - Find $3 a + 2 b$ when $a = 2$ , $b = 5$

$3 (2) + 2 (5) = 6 + 10 = 16$

Example 4: With negative numbers - Find $2 x - 5$ when $x = - 3$

$2 (- 3) - 5 = - 6 - 5 = - 11$ (use brackets!)

Important Notes

Use brackets: When substituting negative numbers: $x - 3$ when $x = - 2$ becomes $(- 2) - 3$
Follow BODMAS: Powers/orders before multiplication/division before addition/subtraction
Show your work: Write the substitution step and calculation step separately

Common Mistakes:

Forgetting brackets with negative numbers causes sign errors: $x + 3$ when $x = - 2$ should be $(- 2) + 3$ , not $- 2 + 3$ (ambiguous)
Miscalculating powers: $2^{2} = 4$ , not 2x2 = wrong interpretation
Not following order of operations: Always do powers before multiplication
Losing track of multiple substitutions in complex expressions